How to keep the correct time and keep your computers synchronized without abusing time servers, using NTP and systemd.

What Time is It?

Linux is funky when it comes to telling the time. You might think that the time tells the time, but it doesn't because it is a timer that measures how long a process runs. To get the time, you run the date command, and to view more than one date, you use cal.
Timestamps on files are also a source of confusion as they are
typically displayed in two different ways, depending on your distro
defaults. This example is from Ubuntu 16.04 LTS:

Some display the year, some display the time, which makes
ordering your files rather a mess. The GNU default is files dated within
the last six months display the time instead of the year. I suppose
there is a reason for this. If your Linux does this, try ls -l --time-style=long-iso to display the timestamps all the same way, sorted alphabetically. See How to Change the Linux Date and Time: Simple Commands to learn all manner of fascinating ways to manage the time on Linux.

Check Current Settings

NTP, the network time protocol, is the old-fashioned way of keeping correct time on computers. ntpd,
the NTP daemon, periodically queries a public time server and adjusts
your system time as needed. It's a simple lightweight protocol that is
easy to set up for basic use. Systemd has barged into NTP territory with
the systemd-timesyncd.service, which acts as a client to ntpd.
Before messing with NTP, let's take a minute to check that current time settings are correct.
There are (at least) two timekeepers on your system: system time,
which is managed by the Linux kernel, and the hardware clock on your
motherboard, which is also called the real-time clock (RTC). When you
enter your system BIOS, you see the hardware clock time and you can
change its settings. When you install a new Linux, and in some graphical
time managers, you are asked if you want your RTC set to the UTC
(Coordinated Universal Time) zone. It should be set to UTC, because all
time zone and daylight savings time calculations are based on UTC. Use
the hwclock command to check:

"Hardware clock is kept in UTC time" confirms that your RTC is
on UTC, even though it translates the time to your local time. If it
were set to local time it would report "Hardware clock is kept in local
time."
You should have a /etc/adjtime file. If you don't, sync your RTC to system time:

$ sudo hwclock -w

This should generate the file, and the contents should look like this example:

$ cat /etc/adjtime
0.000000 1516661953 0.000000
1516661953
UTC

The new-fangled systemd way is to run timedatectl, which does not need root permissions:

"RTC in local TZ: no" confirms that it is on UTC time. What if
it is on local time? There are, as always, multiple ways to change it.
The easy way is with a nice graphical configuration tool, like YaST in
openSUSE. You can use timedatectl:

$ timedatectl set-local-rtc 0

Or edit /etc/adjtime, replacing UTC with LOCAL.

systemd-timesyncd Client

Now I'm tired, and we've just gotten to the good part. Who knew
timekeeping was so complex? We haven't even scratched the surface; read man 8 hwclock to get an idea of how time is kept on computers.
Systemd provides the systemd-timesyncd.service client, which queries remote time servers and adjusts your system time. Configure your servers in /etc/systemd/timesyncd.conf. Most Linux distributions provide a default configuration that points to time servers that they maintain, like Fedora:

[Time]
#NTP=
#FallbackNTP=0.fedora.pool.ntp.org 1.fedora.pool.ntp.org

You may enter any other servers you desire, such as your own local NTP server, on the NTP= line in a space-delimited list. (Remember to uncomment this line.) Anything you put on the NTP= line overrides the fallback.
What if you are not using systemd? Then you need only NTP.

Setting up NTP Server and Client

It is a good practice to set up your own LAN NTP server, so that you
are not pummeling public NTP servers from all of your computers. On most
Linuxes NTP comes in the ntp package, and most of them provide /etc/ntp.conf to configure the service. Consult NTP Pool Time Servers to find the NTP server pool that is appropriate for your region. Then enter 4-5 servers in your /etc/ntp.conf file, with each server on its own line:

The driftfile tells ntpd where to
store the information it needs to quickly synchronize your system clock
with the time servers at startup, and your logs should have their own
home instead of getting dumped into the syslog. Use your Linux
distribution defaults for these files if it provides them.
Now start the daemon; on most Linuxes this is sudo systemctl start ntpd. Let it run for a few minutes, then check its status:

I have no idea what any of that means, other than your daemon
is talking to the remote time servers, and that is what you want. To
permanently enable it, run sudo systemctl enable ntpd. If your Linux doesn't use systemd then it is your homework to figure out how to run ntpd.
Now you can set up systemd-timesyncd on your other LAN hosts to use your local NTP server, or install NTP on them and enter your local server in their /etc/ntp.conf files.
NTP servers take a beating, and demand continually increases. You can
help by running your own public NTP server. Come back next week to
learn how.Learn more about Linux through the free "Introduction to Linux" course from The Linux Foundation and edX.